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\int x^{3}+5\mathrm{d}x
Evaluate the indefinite integral first.
\int x^{3}\mathrm{d}x+\int 5\mathrm{d}x
Integrate the sum term by term.
\frac{x^{4}}{4}+\int 5\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.
\frac{x^{4}}{4}+5x
Find the integral of 5 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{7^{4}}{4}+5\times 7-\left(\frac{5^{4}}{4}+5\times 5\right)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
454
Simplify.
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